Rough $Delta mathcal{I}-$Convergence

Authors : Hafize GUMUS, Nihal DEMİR

Pages : 209-216

View : 75 | Download : 11

Publication Date : 2021-04-28

Article Type : Research Paper

Abstract :In this paper, we study the concept of rough $\mathcal{I}-$convergence for difference sequences in $\leftinsert ignore into journalissuearticles values( \mathbb{R}^{n},\left\Vert .\right\Vert \right); $ where $ \mathbb{R}^{n}$ denotes the real $n-$dimensional space with the norm $\left\Vert .\right\Vert $. At the same time, we examine some basic properties of the set $\mathcal{I}-\lim_{\Delta x_{I}}^{r}=\lbrace x_{\ast}\in\mathbb{R}^{n}:\Delta x_{i}\overset{r}{\rightarrow}x_{\ast}\rbrace $ which is called as $r$-$\mathcal{I-}$ limit set of the difference sequence $\leftinsert ignore into journalissuearticles values( \Delta x_{i}\right); $ and we give some properties of $\mathcal{I}-\lim \inf \Delta x_{i},$ $\mathcal{I}-\lim \sup \Delta x_{i}$ and $\mathcal{I}-$core$\left\{ \Delta x_{i}\right\} .$
Keywords : Statistical convergence, I convergence, rough convergence, difference sequences, I limit point set, I core

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